Ireland has been one of Manchester City's most consistent performers in recent seasons, although the vast number of stars in the club's squad restricted him to just 16 league starts last term.
City have continued to strengthen this summer after bringing in Yaya Toure, David Silva and Jerome Boateng, limiting possible first-team opportunites for Ireland even further.
Black Cats assistant Eric Black admits the club are firm admirers of the 23-year-old, but feel his reported weekly wage of £60,000-a-week, which is due to rise to £80,000-a-week under the terms of his five-year contract, falls outside the North-East club's structure.
"It would be wonderful to bring a player like Stephen Ireland to the club," explained Black.
"I think everybody is aware of how good a player he is, but we have a certain level of salary, which his probably exceeds."